Per centum turned hundredths into everyday comparison language
A percentage expresses a ratio as parts per hundred—45% means 45/100 or 0.45. Latin per centum supplies the name; Rome already taxed auction sales at 1/100 (centesima rerum venalium). Values need not stay between 0 and 100; 111% or −35% appear in change talk.
The word comes from Latin per centum, and the sign grew out of the Italian per cento: the 'per' shrank to 'p.' and then vanished, while 'cento' collapsed into two circles split by a horizontal stroke, the ancestor of %. Abbreviations such as pct. and pc also turn up. Although a percentage is a dimensionless pure number, it is spelled and used like a unit, and the per mille sign ‰ applies the same idea to thousandths.
Reckoning in hundredths is older than decimals, as the Augustan auction levy shows. As medieval money denominations multiplied, calculations over 100 became standard, and by the late fifteenth and early sixteenth centuries arithmetic books applied them to profit and loss, interest and the Rule of Three. By the seventeenth century interest rates were routinely quoted in hundredths.
To turn a ratio into a percentage, multiply by 100: 50 apples out of 1,250 is 0.04, or 4%. Percentages of percentages multiply, so 50% of 40% is 20%, and order does not matter, since 50% of 20 and 20% of 50 are both 10. Writing 25%/100 is a mistake, because it means 0.0025 rather than 0.25. The base must always be stated: in a college where 60% of students are women, 10% study computer science and 5% of women do, women make up 30% of computer science majors, a calculation closely tied to conditional probability.
Source: Percentage
